A056336 Number of primitive (aperiodic) reversible string structures with n beads using exactly two different colors.

0, 1, 2, 4, 9, 16, 35, 66, 133, 261, 527, 1032, 2079, 4123, 8244, 16440, 32895, 65639, 131327, 262380, 524762, 1049071, 2098175, 4195230, 8390646, 16779231, 33558392, 67112892, 134225919, 268443306

Offset: 1

Author

Marks R. Nester

Keywords

• nonn

Comments

A string and its reverse are considered to be equivalent. Permuting the colors will not change the structure. Identical to A056331 for n>1.

References

• M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]

Crossrefs

Column 2 of A276544.

Cf. A056318, A056331, A063524.

Programs

Mathematica

a[1] = 0;
a[n_] := DivisorSum[n, MoebiusMu[#] (2^(n/#-2) + 2^(Floor[n/#/2]-1))&];
Array[a, 30] (* Jean-François Alcover, Jun 29 2018 *)

Formula

a(n) = A056331(n) - A063524(n).